I can't select any CAD surfaces.

Just a guess, but try this

Edit > Graphics Display Window > CAD Elements. Check Surfaces and Set as priority, try selecting the whole cad model with left click hold and drag the box around the model, then hit apply. Not sure if you'll even be able to select the cad at all, even in CAD elements mode, but worth a shot.

Won't let me select surfaces with a click and drag. I brought the same model into a new program, and it works just fine. I'm going to try and save the new program with the functional CAD and copy paste the features from the old program into it. 

Does the box from click and drag even appear? If you're curious to try and fix the old program still, could you check this real quick too? 

Edit > Graphics Display Window > OpenGL > Pan, Zoom, Rotate tab, and make sure PC-DMIS CAD System is selected. This may be a global setting so it may be PC-DMIS already. But hopefully I am wrong.

The PC-DMIS CAD system is selected. I just learned that the CMM programmer that wrote the program, measured his manual features first and then used CAD=Part in his manual alignment which I was told never to use. Maybe that has something to do with the issue.

nope, that SHOULD NOT BE the issue, I use CAD=PART all the time.  Check the SIZE of the .CAD file and make sure you actually HAVE a cad file.  If the program was made using IMPORT ~ CAD by reference, then you don't have a cad file, you have a 'picture' of a cad file.  If it is a cad by reference, it will be 1kb in size.

I think he used Import>CAD but when I deleted the original model and brought it back in, I did a click and drag from the File Explorer window. I already deleted his program and replaced it with mine so I can't check the size of the CAD file.

you can still check it, it the source you dragged in was a reference, then the same issue applies.  also, if the cad he imported was a cad/reference, it is still just the picture.